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Abstracts O-Z

Noboru Ohsumi, Institute of Statistical Mathematics, ``Memories of Chikio Hayashi and His Great Achievement'' Abs: TBA Michael Ong, Illinois Institute of Technology, ``The Use and Ab-Use of Financial Data'' Abs: TBA

C. Osswald and F. Brucker, GET-ENST Bretagne, ``Circular Dissimilarities and Hypercycles'' Abs: In this talk, we present a generalization of Robinsonian dissimilarities called circular dissimilarities. As Robinsonian dissimilarities are the dissimilarities whose clusters (the maximal cliques of its threshold graphs) form an interval hypergraph, clusters of a circular dissimilarities form a hypercycle - a hypergraph compatible with a cycle (Quilliot, 1984). We introduce five-points conditions on a linear order that define circular dissimilarities. These dissimilarities form a submodel of the model introduced by Hubert, Arabie and Meulman (1998) who have used circular orders to extend the inequalities defining the Robinsonian dissimilarities. Moreover, we propose an algorithm to recognize hypercycles in $\mathcal{O}(n^4)$ operations, leading to the recognition of circular dissimilarities in $\mathcal{O}(n^5)$ operations. Barthélemy and Brucker (2001) have shown that approximating a given dissimilarity by a circular dissimilarity is NP-hard. Finally, we propose a heuristic to produce a circular dissimilarity compatible with a given order in $\mathcal{O}(n^4)$ operations, and illustrate our model with a few examples.

Kutluhan Kemal Pak and Edwin Diday, Univeristé Paris IX-Dauphine, ``Construction of Spatial Hierarchies'' Abs: The goal of this work is to extend the traditional hierarchical clustering to spatial hierarchies based on a grid. First we show that a spatial hierarchy induces a kind of dissimilarity called Yadidean defined in Diday (IFCS'2004). Second, we present an ascending algorithm starting from a symbolic data file (which contains as a special case, the standard data). This algorithm gives as output, a spatial hierarchy where each cluster is a convex of the grid and is modelled by a symbolic object. Finally we discuss about the properties of the constructed spatial hierarchy, its quality, and the compatibility between the Yadidean dissimilarity and the grid. The program written in C++, has a graphic tool which is carried out using the OpenGL library. We give several tools for the interpretation. The resulting spatial hierarchy is a 3D graphic that can be rotated and zoomed. Each cluster of the hierarchy has its own colour depending on its height and the individuals who belong to the grid can be interactively interpreted in several ways.

Barbara Japelj Pavesic, Educational Research Institute, Simona KorenjakCerne, University of Ljubljana, and Vladimir Batagelj, University of Ljubljana, ``An Application of Symbolic Clustering Methods on the TIMSS Dataset'' Abs: Is teaching mathematics culturally independent? Trends in Interna tional Mathematics and Science Study, TIMSS, collected information from students and teachers from different countries all over the world to describe differences in teaching mathematics. In the paper, the teachers' and students' datasets, collected in TIMSS 1999 from 37 participating countries, are combined into a single dataset. In this dataset, teachers are described as symbolic objects, including the distributions of their students' answers about the activities during mathematics lessons. Based on this descriptions the adapted leaders method was used to partition all teachers into clusters. The connections between the clusters are presented with dendrogram, based on the adapted Ward's method. The analysis of characteristic properties of clusters' leaders provide some answers to the initial question.

Jean-Yves Pirçon and Jean-Paul Rasson, University of Namur, ``The Last Step of a New Divisive Monothetic Clustering Method: The Gluing-Back Criterion'' Abs: Pirçon and Rasson (2003) propose a divisive monothetic clustering method. In that work, the selection of relevant variables is performed simultaneously with the formation of clusters. The method treats only one variable at each stage; a single variable is chosen to split a cluster into two sub-clusters. Then the sub-clusters are successively split until a stopping criterion is satisfied. The original splitting criterion is the solution of a maximum likelihood problem conditional on the fact that data are generated by a nonhomogeneous Poisson process on two disjoint intervals. The criterion splits at the place of the maximum integrated intensity between two consecutive points. This paper extends Pirçon and Rasson (2003) by developing a ``gluing-back'' criterion. The previous work explained the new method for combining trees and nonhomogeneous Poisson processes and the splitting criterion. It was shown that the maximum likelihood criterion reduces to minimization of the integrated intensity on the domain containing all of the points. This method of clustering is indexed, divisive and monothetic hierarchical, but its performance can be improved through a gluing-back criterion. That criterion is developed in this paper, after a brief review of the main ideas.

Jennifer Pittman and Mike West, Duke University, ``Issues in Bayesian Tree Modeling of Clinical and Gene Expression Data'' Abs: Recent studies have demonstrated the usefulness of gene expression information in the search for improved diagnostic and prognostic tools as a part of overall cancer treatment. For example, gene expression profiles have been used to more accurately predict patient outcome in comparison to clinical indicators while the clustering of breast carcinomas by gene expression patterns has also been shown to be highly correlated with both overall and relapse-free survival. We have developed an approach to the analysis and modeling of clinical and gene expression data based on Bayesian tree models. Our current aim is to generate classification tree models which can exploit such data to characterize clinical states and predict cancer-related outcomes for patients of interest. Through cross-validation this Bayesian tree approach provides an honest measure of the uncertainty or accuracy of these predictions. Providing a measure of accuracy is critical, as it provides information regarding the quality or value of such predictions. The development and generation of our models involves statistical issues such as the specification a Bayesian model for the data, the choice of a measure to determine tree growth, and the selection of a method for searching through the tree model space. This talk will focus on a discussion of these issues in the context of Bayesian predictive classification tree analyses. Applications of our models to the predictive analysis of outcomes in breast cancer and ovarian cancer will be presented.

Margaret Polinkovsky, Duke University, ``Analysis of Key Comparisons'' Abs: TBA

Robert C. Powers, University of Louisville, ``Consensus Functions on Hierarchies that Satisfy Independence and Pareto'' Abs: Let $\mathcal{H}$ be the set of all hierarchies on a finite set $S$. A consensus function on $\mathcal{H}$ is a map $C : \mathcal{H}^k \rightarrow \mathcal{H}$ where $k \ge 2$. A consensus function $C$ satisfies independence if, whenever two profiles agree when restricted to a subset $X$ of $S$, then the corresponding consensus outputs agree when restricted to $X$. If $C$ preserves unanimity with respect to clusters, then $C$ is said to satisfy the Pareto condition. Barthélemey et al. (1991) gave an example of a consensus function $C$ on $\mathcal{H}$ such that $C$ satisfies independence, Pareto, and is not a dictatorship. The surprising nature of this example leads to the following problem. Give a complete description of all the consensus functions on $\mathcal{H}$ that satisfy independence and Pareto. I will present some recent work that provides a partial solution to this problem.

Carey Priebe, Johns Hopkins University, ``Applying the Class Cover Catch Digraph Classifier'' Abs: We describe an extension of the Class Cover Catch Digraph (CCCD) classifier, specifically designed for detection problems--two-class classification problems in which the natural priors on the classes are severely skewed. The emphasis of our approach is on computationally efficient classification for real-time applications. Our principal contribution is a boosted tree classifier built upon the CCCD structure. This classifier achieves performance comparable to that of the original CCCD classifier, but at drastically reduced computational expense. An analysis of classification performance and computational cost is performed using data from a face detection application. Comparisons are provided with Support Vector Machines (SVMs). These comparisons show that while some SVMs may achieve superior classification performance, their computational burden is so high as to make them unusable in real-time applications. On the other hand, our proposed classifiers combine high detection performance with extremely fast classification.

Sarnath Ramnath, Mynul H. Khan, and Subair Shams, St. Cloud State University, ``New Approaches for Sum-of-Distances Clustering'' Abs: It was shown recently that by employing ideas from incremental graph connectivity the asymptotic complexity of sum-of-diameters bipartitioning could be reduced. This article further exploits this idea to develop simpler algorithms and reports on an experimental comparison of all algorithms for this problem.

Jim Ramsay, McGill University, ``Modeling the Evolution of Disease Symptoms with Principal Differential Analysis'' Abs: This talk describes the application of functional data analysis techniques to study the course of systemic lupus erythematosus in a sample of patients. The method models patient histories by fitting a pair of differential equations to the data. The purpose is to predict the duration of a flare-up and its speed of onset. Jean-Paul Rasson and Pascale Lallemand, Facultés Universitaires Notre-Dame de la Paix, ``Clustering Trees Applied to Symbolic Objects'' Abs: The present method is a divisive clustering method for symbolic data. By definition of a divisive clustering method, the algorithm starts with all objects in one cluster, and splits successively each cluster into (two) smaller ones until a suitable stopping rule prevents further divisions. This algorithm proceeds also in a monothetic way. In other words, the algorithm assumes as input $n$ data vectors and proceeds such that each split is carried out by using only one single variable (which is selected optimally). The aim of our work is to build a recursive algorithm for sharing a given population of symbolic objects into classes. The original contribution of this method lies in the way of splitting a node. Indeed, the cut will be based on the only assumption that the distributions of points can be modeled by non-homogeneous Poisson process where the intensity will be estimated by the kernel method. The cut will be made in order to maximize the likelihood function.

Jean-Paul Rasson and Laurent Sancinito Spito, University of Namur, ``Partitioning Non-Convex Clusters Using Alpha-Shapes'' Abs: The aim of our work is to propose a new partitionning method and a new discriminant rule for the basic space $\hbox{{I}\kern-.1667em\hbox{R}}^2$. We introduce the concept of internally path connected bodies, which allow us to relax the convexity hypothesis of the hypervolume method (Rasson, Hardy (1982)). Our wish is to generalize the latter because of its failure in finding non convex natural classes. We try to build unsupervised and supervised classification rules and algorithms, based on this new assumption, with the help of a tool that generalizes the convex hull of a set of points : the alpha-shape. The generalization to $\hbox{{I}\kern-.1667em\hbox{R}}^d$ of the hypotheses we make and the tools we use is straightforward.

Gunter Ritter and María Teresa Gallegos, Universität Passau, ``Clustering of Contaminated and Ambiguous Data'' Abs: We present a number of clustering algorithms for Euclidean data with outliers. Besides outlier treatment by trimming, as an additional novelty we allow the data to be ambiguous. This means that each object may be represented by more than one feature set (variant), only one of which is valid (the regular variant), (2). In addition to clustering and outlier removal, the algorithms automatically select the regular variants of the objects. The algorithms are based on mixed MAP-ML-criteria, MAP with respect to variant selection and ML with respect to outlier detection and the distribution parameters. They are most efficient if the ML-estimator of these parameters has a simple form. This is the case with various normal data models. The algorithms have the usual EM flavor and combine ML clustering with Rousseeuw's minimum covariance determinant estimator, cf. Pesch (1) and Rousseeuw and Van Driessen (3). We illustrate the results by simulation studies and applications to real data sets.

O. Rodríguez, University of Costa Rica, W. Castillo, University of Costa Rica, E. Diday, University of Paris IX-Dauphine, and J. González, University of Costa Rica, ``Correspondence Factorial Analysis for Symbolic Multi-Valued Variables'' Abs: In this paper a new method and two new algorithms for Correspondence Factorial Analysis when we have Symbolic Multi-Valued Variables (CFASym) are proposed. The method is illustrated with an example, which was built using the module CFASym in PIMAD-Symbolique, developed by the authors.

Ingo Ruczinski, Johns Hopkins University, ``Improvements for Logic Regression'' Abs: Logic Regression was recently introduced as a novel regression method and classification tool. This adaptive methodology is based on new predictors being generated as Boolean combinations from binary covariates, and hence models with high order interactions can be explored. We show some public health related case studies, highlight the differences to related methodologies such as CART, MARS and Random Forests, and report some recent improvements in the methodology (such as measures of variable importance obtained from MCMC based algorithms) and the software (in particular, the LogicReg R package).

Takahiro Saito, Hosei University, Kenji Nagasaka, Hosei University, and Tomokazu Takahashi, Aoyamagakuin University, ``Classification Problems for Story Animations'' Abs: There are two kinds of animations (manga in Japanese), one of which is animated cartoon and another is animated story (i.e. story with pictures). We treat animated stories from a single author, Akira Toriyama, especially his master work ``DRAGON BALL''. From the usages of imitative words and/or onomatoeic words, we can estimate the produced period and also who assisted the production. From the point of copyright, an important issue is how to detect discriminate the originals and forgery to which we will apply image processing tool and theory of statistics.

Gilbert Saporta, CNAM Paris, and Cristian Preda, Université de Lille, ``Clusterwise PLS Regression with Applications to Functional Data'' Abs: The Partial Least Squares (PLS) approach is used for the clusterwise linear regression algorithm when the set of predictor variables forms an $L_{2}$-continuous stochastic process. The number of clusters is treated as unknown and the convergence of the clusterwise algorithm is discussed. The approach is compared with other methods via an application to stock-exchange data.

Yoshiharu Sato, Hokkaido University, ``Clustering Binary Data Using a Transformation into Directional Data'' Abs: Binary data is defined as a set of observed values whose attributes take the binary value, usually, denoted by 0 or 1. Recently, the number of attributes and objects become extremely large due to the progress of the observation and information technology. Then it is difficult to apply the traditional hierarchical clustering methods. The feasible methods are limited for the required size of memory and computational costs. Among the clustering methods, the k-means method and its modification are frequently used for the large data set,because of the comparatively low requirements. In binary data, the most crucial point is a definition of the center of each cluster. In several papers, the concept of a mode is used, and the clusters are constructed using parallel algorithm with k-means method. However, the mode does not determine uniquely. Moreover, in k-means method, a concept of the within variance of each cluster is important for the criterion of the clustering. This is closely connected with the used similarity measure between objects. Then, for the natural definition of the mean and variance, we transform the binary data to directional data. Using the concept of the descriptive measures for the directional data, we extend the k-means method to binary data.

Jan Schepers$\;$ and Iven Van Mechelen, University of Leuven, ``Three-Mode Partitioning: An Evaluation of Three Algorithms'' Abs: In this paper, a simultaneous clustering method for three-way three- mode data is presented in which the simultaneous clusterings are restricted to be partitions of the modes involved in the data. The proposed method is an extension of existing simultaneous partitioning methods for two-way two-mode data. To retrieve the best approximation between the reproduced and the actual three- dimensional data array, a least squares optimization algorithm is proposed. In a simulation study, the overall performance of the algorithm is discussed and compared to the algorithms recently proposed by Rocci and Vichi (2003) and Kiers (2004).

Alexander Schliep, Christine Steinhoff, and Alexander Schoenhuth, Max Planck Institute, ``Inference of Groups in Gene Expression'' Abs: The analysis of gene expression time-courses poses many methodological challenges due to the complexity of the regulatory interactions producing the observables, their inherent variability and the levels of noise present even under optimal experimental conditions. On account of the exploratory nature of the analysis, the questions asked change frequently, as do prior knowledge and beliefs. Effective methods should reflect those constraints as well as the interactive fashion in which the analysis is often performed. We propose to use a mixture of Hidden Markov Models (HMMs) to find groups in gene expression time course datasets. Mixtures have a number of preferable properties. In contrast to clustering, genes do not have to be partitioned into groups, rather the frequent ambiguity of function or regulation can be accounted for. They also exhibit a higher degree of robustness with respect to noise and afford a simple, entropy-based diagnostic for the level of ambiguity in assignments to groups given the mixture. The HMMs used prove effective in modeling the qualitative behavior of time-course data, as they reflect the time-dependencies of measurements and allow to capture subtle signals. Lags and the varying speeds at which the regulatory programs are executed can be handled; simple variants can be used to deal with further questions of biological interest. We present the mixture framework and the estimation method used. Partially supervised learning makes use of prior information with respect to membership of genes in the same or distinct groups. A heuristic for proposing an initial collection of HMMs and modifying HMMs during the training is discussed, as well as an algorithm to partition an inferred group into synchronous subgroups. The performance of our approach is evaluated on artificial and biological expression data. We conclude with computational aspects of our implementation of the method.

Teppei Shimamura, $\,$ Hiroyuki Minami, and Masahiro Mizuta, Hokkaido University, ``Nonlinear Regression Modeling Strategy Based on Radial Basis Function Networks and Absolute Shrinkage'' Abs: Neural networks provide a flexible model for extracting usefulinformation from highly complicated data and give good performance overa wide range of applications. We consider the construction of nonlinearregression models with radial basis function networks and maximumpenalized likelihood methods. In the modeling process, it is crucial howwe choose the number of the basis functions, the positions of thecentres, the smoothing parameter, and the regularization parameter. Ifcare is taken not to choose these parameters, the estimated model oftengives poor generalization performance.We propose a new regression modeling strategy based on radial basisfunction networks; choosing as centres the parameters resulting from anormal mixture model of the underlying conditional distribution $p(x\vert y)$,and estimating the weights by maximum penalized log-likelihood withLasso penalty. Furthermore, we give an information criteria for modelevaluation and apply it to choose the optimal smoothing paremeter andregularization parameter. We investigate the performance of the proposedprocedure and compare it with traditional methods through simulations.The results show the proposed model performs well and has someadvantages over traditional methods.

Ahu Sieg, Bamshad Mobasher, and Robin Burke, DePaul University, ``Inferring User's Information Context from User Profiles and Concept Hierarchies'' Abs: The critical elements that make up a user's information context include the user profiles that reveal long-term interests and trends, the short-term information need as might be expressed in a query, and the semantic knowledge about the domain being investigated. The next generation of intelligent information agents, that can seamlessly integrate these elements into a single framework, are enabled to effectively locate and provide the most appropriate results for users' information needs. In this paper we present one such framework for contextualized information access. We model the problem in the context of our client-side Web agent ARCH (Adaptive Retrieval based on Concept Hierarchies). In ARCH, the user profiles are generated using an unsupervised document clustering technique. These profiles, in turn, are used to automatically learn the semantic context of user's information need from a domain-specific concept hierarchy. Our experimental results show that implicit measures of user interests, combined with the semantic knowledge embedded in a concept hierarchy, can be used effectively to infer the user context and improve the results of information retrieval.

Age Smilde, University of Amsterdam and TNO Nutrition and Food Research, Jeroen Jansen, Huub C. J. Hoefsloot, Jan van der Greef, and Marieke E. Timmerman, ``Multiset Methods for Longitudinal Metabolomics Data'' Abs: Metabolomics is a technique that enables quantification and qualitative analysis of metabolites in biological fluids. There is an increasing awareness in the biology community that time-resolved metabolomics measurements contain important information regarding biological organisms. This is, obviously, related to the dynamic nature of organisms resulting in biorhythms. Such biorhythms can be disturbed by external causes (e.g. drug intake, food intake) or internal causes (e.g. developing diseases). Such disturbances affect the metabolism of organisms and are expected to show up in properly measured longitudinal metabolomics data (e.g. in the urine or blood of the organism). Longitudinal metabolomics analysis can serve several goals. In normality studies, the goal is to establish biorhythms under homeostasis which serve as a reference point to detect future deviating dynamic behavior. Another goal is to detect early biomarkers for developing diseases; this calls for models based upon which biomarker selection can take place. Yet another goal is to model the dynamic response of an organism to external stress which gives insight in the way such an external stress influences the system. All these goals require a different data analysis method. The type of method depends also on the set-up of the metabolomics data set. An overview is given of different longitudinal modeling strategies for metabolomics data. These methods are based on three-way analysis and (multilevel) simultaneous component analysis. Examples will be given using i) a longitudinal normality study of monkey urine and ii) a longitudinal metabolomic diabetes II study of blood serum. The strengths and limitations of the methods will be illustrated with these example studies.

Mike Steel, University of Canterbury, New Zealand, ``Phylogenetic Closure Operations and Homoplasy-Free Evolution'' Abs: Phylogenetic closure operations on partial splits and quartet trees turn out to be both mathematically interesting and computationally useful. Although these operations were defined two decades ago, until recently little had been established concerning their properties. Here we present some further new results and links between these closure operations, and show how they can be applied in phylogeny reconstruction and enumeration. Using the operations we study how effectively one may be able to reconstruct phylogenies from evolved multi-state characters that take values in a large state space (such as may arise with certain genomic data).

Russell Steele, McGill University, and Luis Garcia, Virginia Tech University, ``Algebraic Geometry and Model Selection'' Abs: Recent advancements in the machine learning community have been made in the application of algebraic geometry to Bayesian model selection for neural networks. Rusakov and Geiger (2003), using results from Watanabe (2001), present a new asymptotic approximation to the integrated likelihood for Naive Bayes networks. The key to the approximation is an attempt to correct the standard dimensionality penalty for the BIC to reflect the ``true'' effective dimensionality of the model. However, only limited work has been done to interpret these results with respect to current work on effective dimensionality in Bayesian research, particularly, in light of the currently widespread use of the DIC (Spiegelhalter, et al., 2002). In this talk, the speaker presents the basic idea behind the Rusakov/Geiger approximation, compares their approximation to the actual integrated likelihood, and links these results to what the DIC presumably is trying to estimate. The speaker will conclude with discussion of how these results for Naive Bayes networks may possibly be used to improve integrated likelihood calculations for other statistical models.

Douglas Steinley, University of Illinois at Urbana-Champaign, ``Standardizing Variables in k-Means Clustering'' Abs: Several standardization methods are investigated in conjunction with the $K$-means algorithm under various conditions. We find that traditional standardization methods (i.e., $z$-scores) are inferior to alternative standardization methods. Future suggestions concerning the combination of standardization and variable selection are considered.

Akinobu Takeuchi, Jissen Women's University, Takayuki Saito, Tokyo Institute of Technology, and Hiroshi Yadohisa, Kagoshima University, ``Extension of Average Linkage Clustering to Asymmetric Data'' Abs: TBA

Basavanneppa Tallur, University of Rennes 1, ``Hierarchical Clustering of Binary Attribute Data Based on Correlation with Application to Bioinformatics'' Abs: Cluster analysis is among the most useful data analysis tools in all fields of scientific research. There exist a great number of methods and software tools for performing cluster analysis and, a typical data set is contained in a data table whose rows represent 'observations' (or 'individuals') and columns, the 'variables' (or 'attributes'). The following three elements are of crucial importance in building a hierarchical clustering method: 1. a suitable mathematical representation of data that takes into account the nature (or type) of the attributes; 2. a measure of distance (or similarity) between observations and/or attributes depending on whether one intends to cluster the set of observations, attributes, or both; 3. the cluster joining criterion. The binary attributes are naturally present in many application dommains (and almost all other types of data may be easily transformed into binary attributes). The literature is rich with hundreds of similarity measures for such data but most of them are 'biased' and unfit to be used directly in clustering algorithms. We propose a similarity index for this type of data that has been derived starting from the the 'observation profiles' representation of data akin to the one used in correspondence analysis, and is based on the concept of correlation between variables. The cluster joining criterion is also coherent with data representation and this combination has led to a very elegant and efficient clustering method. This method has been tested on various real world data and compared with some classical methods. We will describe one of our latest applications in bioinformatics.

Tao Tao and ChengXiang Zhai, University of Illinois at Urbana-Champaign, ``A Mixture Clustering Model for Pseudo Feedback in Information Retrieval'' Abs: In this paper, we present a new mixture model for performing pseudo feedback for information retrieval. The basic idea is to treat the words in each feedback document as observations from a two-component multinomial mixture model, where one component is a topic model anchored to the original query model through a prior and the other is fixed to some background word distribution. We estimate the topic model based on the feedback documents and use it as a new query model for ranking documents.

Michel Tenenhaus, HEC Business School, ``PLS Path Modeling for Multiple Table Analysis'' Abs: A situation where $J$ blocks of variables are observed on the same set of individuals is considered in this paper. A factor analysis logic is applied to tables instead of individuals. The latent variables of each block should explain their own block well and at the same time the latent variables of the same rank should be as positively correlated as possible. In the first part of the paper we describe the hierarchical PLS path model and review the fact that it allows one to recover the usual multiple table analysis methods. In the second part we suppose that the number of latent variables can be different from one block to another and that these latent variables are orthogonal. PLS regression and PLS path modeling are used for this situation. This approach is illustrated by an example from sensory analysis.

F. Goupil-Testu, M. Touati, I. Wagne, Université of Paris IX-Dauphine, A. Pelc, CCMSA, and E. Diday, Université of Paris IX-Dauphine, ``Analysis of Drug Dispensing with Symbolic Methods'' Abs: This work is a study of the dispensing of drugs to people over 70 years old, affiliated to the Caisse Centrale de la Mutualite Sociale Agricole (CCMSA), the head of french social security organization (MSA) covering the agricultural area. The CCMSA stores yearly about 130 million records of payment operations in its data warehouse. These records accurately reflect the operations related to the 8.7 billion euros paid to the affiliates, for Sickness - Maternity - Work injuries. The aim is to improve the risk management. The basic idea is to aggregate the initial elementary data into more complex data , called "concepts" modeled by "symbolic objects", and apply to these new data types an extension of the classical data analysis methods called "Symbolic Data Analysis". There has been a drastic reduction of the data, with a minimal information loss, since the individual data relating to the people belonging to the concept have been replaced by intervals or probability distributions, also allowing the data handling to keep confidential. For now, the study only takes a limited data sample, coming from the drug payments to the MSA affiliates of the Morbihan department aged over 70, for the fourth quarter of year 2002. So, for the referenced period and area, there are 315724 refunding lines, coming from 81861 prescriptions done by 2249 doctors, for 19541 insured. For instance, among the "high consumers" we find the insured in ALD (long term payment exemption for severe illness), mainly women, who are higher consumers of fully refunded drugs than those of the "low consumers" class. More generally, the advantage of working on concepts is that we reduce the data and we find risk categories keeping confidentiality.

Javier Trejos, Alex Murillo, and Eduardo Piza, University of Costa Rica, ``Clustering by Ant Colony Optimization'' Abs: We use the heuristic known as ant colony optimization in the partitioning problem for improving solutions of k-means method (McQueen (1967)). Each ant in the algorithm is associated with a partition, which is modified by the principles of the heuristic; that is, by the random selection of an element, and the assignment of another element which is chosen according to a probability that depends on the pheromone trail (related to the overall criterion: the maximization of the between-classes variance), and a local criterion (the distance between objects). The pheromone trail is reinforced for those objects that belong to the same class. We present some preliminary results, compared to results of other techniques, such as simulated annealing, genetic algorithms, tabu search, and k-means. Our results are as good as the best of the above methods.

Heather Turner, Trevor Bailey, and Wojtek Krzanowski, University of Exeter, ``The Plaid Model: Some Enhancements and Extensions'' Abs: This talk describes a range of improvements and extensions to the plaid model, a two-way clustering method developed by Lazzeroni and Owen (2002) for analysing gene expression data. The model has a probabilistic ANOVA-type structure, in which the expression level $y_{ij}$ of the $i$th gene in the $j$th sample is given by $y_{ij} = ( \mu_0 + \alpha_{i0} + \beta_{j0}) + \sum_{k=1}^K( \mu_k
+ \alpha_{ik} + \beta_{jk})\rho_{ik}\kappa_{jk} + \epsilon_{ij}. $ Here $k$ indexes each of the $K$ biclusters, $0$ indexes the background, $\rho_{ik}$ and $\kappa_{jk}$ are indicators that show presence or absence of gene $i$ and sample $j$ in bicluster $k$, and $\mu, \alpha, \beta$ are mean, gene and sample effects respectively. In the first part of the talk we briefly survey biclustering of microarray data, introduce the plaid model, outline the original method of fitting it, and describe an alternative approach based on the SINDCLUS algorithm (Chaturvedi and Carroll, 1994). The alternative method shows improved efficiency when tested against the original method on simulated microarray data. In the second part of the talk we then consider several modifications to the model itself. First, grouping information can be incorporated to allow partial supervision of the clustering process, favouring more interpretable clusters. Second, extra parameters can be added to the model when each gene/sample combination contains repeated measurements, usually over time. This enables three-way data to be analysed, avoiding the loss of information produced by collapsing complex datasets. Computing implications are discussed, and real data examples are used to illustrate all the proposed extensions.

Iven van Mechelen, Catholic University of Leuven, ``Three-Way Classification Models: An Overview'' Abs: In this paper, I will present a structured overview of models and data-analytic methods for three-way three-mode data that imply a clustering of one or more modes of the data. This overview was inspired by the pioneering work of Hartigan (1972, 1975), and links up with a recent comprehensive taxonomy of the two-mode clustering domain (Van Mechelen, Bock, & De Boeck, in press). Key structuring principles of the overview include: (1) the number of modes that are simultaneously clustered -one, two or all three- (with for the possibly nonclustered mode(s) the option of an additional simultaneous dimensional reduction), (2) whether the data clusterings implied by the methods are partitions, nested hierarchies or overlapping clusterings, and (3) whether the methods are based on a deterministic or on a stochastic (mixture or fixed-classification) model. Existing clustering methods for three-way three-mode data (and their interrelations) will be located in the overview, including three-way tandem analysis, three-way mixture modeling, weighted ultrametric trees, three-way GENNCLUS, three-mode partitioning, three-mode hierarchical cluster analysis, three-mode overlapping CANDCLUS, and three-way hierarchical classes modeling. In addition, several still to be developed methods as implied by the taxonomy will be pointed at as well.

Bart Jan van Os, Leiden University, ``Globally Optimal Partitioning by Dynamic Programing'' Abs: Nonexhaustive partitioning problems may arise in at least two psychometric areas. First, nonexhaustive clustering proposes to cluster only a subset of the objects under study. Such approaches are most popular in pattern recognition (Theodoridis and Koutroumbas, 1998) and bioinformatics (de Bruin, 1998), where they are combined with fast sequential algorithms, but they may also be used in other areas. Objectives for nonexhaustive clustering might be the need of a few small prototypical clusters, or the avoidance of outlier influence on the clusters solution and it's quality assessment. In this talk a globally optimal approach to (small) non-exhaustive partitioning problems will be pursued. In such an approach, the objective is to maximize the sum of some (homogeneity) function of the individual clusters/tests, without the necessity to include all objects/items in the solution. Special care in formulating this objective function is to be taken to avoid including to few or to many objects/items. To solve this problem globally optimal, two approaches to an exact Dynamic Programming algorithm are presented. The algorithm will be applied to a dataset involving employement in nine different industries in 22 selected European countries during the Cold War.

Mark Vangel, Massachusetts General Hospital and Harvard University, ``Combining Functional MRI Data on Multiple Subjects'' Abs: Worsley et al. (2002) propose a practical approach to multiple-subject functional MRI data analyses which uses the EM algorithm to estimate the between-subject variance component at each voxel. The main result of this article is a demonstration that the much more efficient Newton-Raphson algorithm can be reliably used for these calculations. This result follows from an extension of a simple algorithm proposed by Mandel and Paule (1970) for the one-way unbalanced ANOVA model, two variants of which have been shown to be equivalent to modified ML and REML, in which the ``modification'' is that the within-subject variances as treated as known.

Vladimir Vapnik, AT&T, Title TBA

Maurizio Vichi and Roberto Rocci, University ``La Sapienza'' and University ``Tor Vergata'' of Rome, ``Multimode Clustering'' Abs: In this paper, new methodologies for multi-mode clustering of a two- (three-) way data set are proposed. The two- (three-) mode clustering model, here adopted, is as a collection of disjoint object and variable clusters (object, variable and occasion clusters), identifying a data matrix (array) which is split into disjoint blocks of sub-matrices (sub-arrays), where entries within blocks change only for a random residual. When the multimode clustering degenerates into the clustering of the objects only, and the model is estimated with a least-squares loss function, the methodology reduces to the well-known k-means algorithm (Mac Queen 1967). In this paper, the two- (three-) mode clustering model is estimated under the model-free assumptions in a least-squares context, by using an new algorithm, which is named double (triple) k-means. First, we show how to estimate the two- (three-) mode clustering model by using sequential procedures based on the k-means algorithm. We observe that these procedures generally give non optimal estimations of the two- (three-) mode model. Efficient alternating least-squares (ALS) algorithms are then proposed. Hence, the sequential procedures will be used as useful starting point for the ALS algorithms. A simulation study to test the performances of the algorithms will also be presented. It is well-known that k-means algorithm frequently stops to local minima solutions. Therefore, we will test how this problem is severe in our algorithms. In the case clusters of objects and variables are well- separated, the problem is solved -for data sets with dimension (1000 objects ´ 400 variables)- by using 15 random initial solutions and by retaining among these the best result. When the error level added to the model is very high the generated solution is not any more formed by well-separated clusters. In fact, the best solution given by the algorithm was always better than that generated, when the number of initial random starts was fixed equal to 30. It is interesting to note that double and triple k-means maintain the feature of the k-means to be fast algorithms applicable also to very large data sets.

Kiri Wagstaff, Jet Propulsion Laboratory, ``Clustering with Missing Values: No Imputation Required'' Abs: Clustering algorithms can identify groups in large data sets, such as star catalogs and hyperspectral images. In general, clustering methods cannot analyze items that have missing data values. Common solutions either fill in the missing values (imputation) or ignore the missing data (marginalization). Imputed values are treated as being just as reliable as the observed data, but they are only as good as the assumptions used to create them. In contrast, we present a method for encoding partially observed features as a set of supplemental soft constraints and introduce the KSC algorithm, which incorporates constraints into the clustering process. In experiments on artificial data and data from the Sloan Digital Sky Survey, we show that soft constraints are an effective way to enable clustering with missing values.

Guenther Walther, R. Tibshirani, D. Botstein, and P. Brown, Stanford University, ``Cluster Validation by Prediction Length'' Abs: We propose a new quantity for assessing the number of groups or clusters in a dataset. The key idea is to view clustering as a supervised classification problem, in which we must also estimate the ``true'' class labels. The resulting ``prediction strength'' measure assesses how many groups can be predicted from the data, and how well. In the process, we develop novel notions of bias and variance for unlabelled data. Prediction strength performs well in simulation studies, and we apply it to clusters of breast cancer samples from a DNA microarray study. Finally, some consistency properties of the method are established.

Leland Wilkinson, SPSS, Inc., ``Streaming Data in Multiple Windows'' Abs: Norton and Wilkinson (2001) introduced a system, called Dancer, for graphing real-time data streams. This talk covers an extension of this system to handle graphing of multiple streams simultaneously in multiple windows. We discuss data fusion mechanisms and rendering models which enable display of multiple streams in real time (up to 10,000 events per second).

Graham Wills, SPSS, Inc., ``Transformations of Graphs'' Abs: The Grammar of Graphics (1999) presents examples of ordinary charts that are embedded in non-rectangular coordinate systems. In many of these examples, structures that are difficult to discern in rectangular coordinates are easier to detect in alternative coordinates. This talk extends the idea of graphing in non-rectangular coordinates to graphing with coordinate transformation chains. We discuss the mechanisms for composing coordinates in a graphics system and present examples that illustrate the usefulness of these methods.

David Wishart, University of St. Andrews, ``Classification of Single Malt Whiskies by Flavour'' Abs: We describe the cardinal flavours that are found in single malt whiskies, and explain how the production and maturation processes influence these flavours. To simplify the comparison of malt whiskies, a standardized profile of 12 cardinal flavours was developed from around 1000 tasting notes and over 500 whisky terms. The principal malt whiskies from all the Scottish distilleries were then profiled and classified by flavour (Wishart, 2000). This helps answer questions like - (1) My store offers a bewildering selection of malt whiskies, so what should I buy? (2) Dad drinks Macallan but I want to give him another malt that's similar in flavour which he will also enjoy? (3) Can you suggest six malts for my cabinet that illustrate the range of single malt whiskies? Whisky Classified: Choosing Single Malts by Flavour is the first book to classify single malt whiskies by flavour. It does not rate whiskies by marks-out-of-ten for quality, or describe them by regional styles. It is a consumer-friendly guide that takes the confusion and guesswork out of whisky-buying, and aims to help the novice or present-buyer make the right purchase of Scotland's national drink. It is also an interesting application of classification methodology for a non-technical readership, and arguably the most widely sold book derived from a product segmentation. This paper extends the previous work by developing TypeAnalyst, a retailing aid to identify the appropriate cluster and nearest neighbours of new whisky expressions. The presentation concludes with a tutored tasting sponsored by Aberfeldy 12yo, Aberlour 10yo, Ardbeg 10yo, Auchentoshan 10yo, Balblair 16yo, Balvenie 12yo, Balvenie DoubleWood 12yo, Benromach 18yo, Bowmore 12yo, Bruichladdich 10yo, Bunnahabhain 10yo, Dalmore 12yo, Deanston 10yo, Edradour 10yo, Glen Deveron 10yo, Glenfarclas 12yo, Glenfiddich 12yo, Glen Garioch 10yo, Glengoyne 10yo, Glenlivet 12yo, Glenmorangie 12yo, Glenmorangie Madeira Finish 12yo, Glenmorangie Sherry Finish 12yo, Glen Moray 10yo, Glenrothes 1989, Highland Park 18yo, Isle of Jura Superstition, Macallan Cask Strength, Laphroaig 10yo, Old Pulteney 12yo, Speyburn 10yo, Springbank 10yo, Strathisla 12yo, Tamdhu 10yo and Tobermoray 10yo.

Wenshang Wu, the University of Illinois at Urbana-Champaign, Clement Yu, University of Illinois at Chicago, and Weiyi Meng, State University of New York at Binghamton, ``Database Selection for Longer Queries'' Abs: In this paper, we propose a new method to construct database representatives and to decide which databases to select for a given query when the query may be long. One critical difference from earlier approaches is that the dependencies of words in documents are captured in the database representatives. Usually, the dependencies are limited to phrases, especially noun phrases.

S. Stanley Young, National Institute of Statistical Sciences, ``The Use of Metabolomic Data to Predict Disease Status'' Abs: Metabolomics is the new `omics' science that concerns biochemistry. A metabolomic dataset includes quantitative measurements of all small molecules, known as metabolites, in a biological sample. These datasets are rich in information regarding dynamic metabolic (or biochemical) networks that are unattainable using classical methods and have great potential, conjointly with other omic data, in understanding the functionality of genes. Herein, we explore a complex metabolomic dataset with the goal of using the metabolic information to correctly classify individuals into different classes. Unfortunately, these datasets incur many statistical challenges: the number of samples is less than the number of metabolites; there is missing data and non-normal data; and there are high correlations among the metabolites. Thus, we investigate the use of robust singular value decomposition, rSVD, and recursive partitioning to understand this metabolomic data set. The dataset consists of 63 samples, in which we know the status of the individuals (disease or normal and for the diseased individuals, if they are on drug or not). Clustering using only the metabolite data is only modestly successful. Using distances generated from multiple tree recursive partitioning is more successful.

Bei Yu, University of Illinois at Urbana-Champaign, ``Discriminating Writing Styles Between Native and Non-Native English Writers'' Abs: Identifying the differences in academic writing between native and non-native speakers is a research problem in second language acquisition and contrastive linguistics. This ongoing project is a computational analysis of the collective writing style differences between the writing of Chinese and English speakers. To formalize this problem as a classification task, research articles written by English and Chinese speakers are represented as vectors of the following normalized style features: common word sequences frequencies, parts-of-speech frequencies and other general style markers such as word length and sentence length, etc. The space of features is then reduced and transformed with the goal of predicting whether the author is English or Chinese speaker. Three classification algorithms are proposed for testing and comparison: decision tree, naive Bayesian and discriminant analysis. Aims include an assessment of the discriminatory power of the features.

Helen Zhang, North Carolina State University, ``Unified Multiclass Proximal Support Vector Machines'' Abs: TBA

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